Two separate paths to the concept of intelligence are discussed: the psychometric path being concerned with the measurement of intelligence, involving the methodology of norm-referenced testing; the path followed by Piaget, and others, addresses from the start the related question of how intelligence can be described, and employs a criterion-referenced methodology. The achievements of psychometrics are briefly described, with an argument that they now remain important tools of what Kuhn called 'normal science'. The criterion-referenced approach of Piaget and others is described, with evidence from intervention studies that the Genevan descriptions of children-in-action have allowed the choice of contexts within which children can profitably be challenged to go further in their thinking. Hence, Genevan psychology is also now a part of the normal science with important uses, shown both in neo-Piagetian studies and further research stemming from Geneva. Discussion of the 'Flynn effect' sheds light on both paths, with problems still unresolved. The argument is then developed that the relevance of neuroscience needs to be discussed to try to decide in what ways it may provide useful insights into intelligence.